v(t) = x'(t)
and
a(t) = v'(t) = x''(t)
, so using our basic calculus rules again we
find that

v(t) = 6t - 8 and a(t) = 6

Notice that the acceleration in this case is constant, and that its value is
equal to twice the coefficient of
t2
in
x(t)
.

Problem :
What happens when a car which is traveling along at constant velocity
screeches to a halt?

The velocity of the car decreases rapidly, corresponding to a large negative
acceleration (or deceleration) of the vehicle (courtesy of good
brakes). While the car was traveling at constant velocity, on the other
hand, the acceleration was zero.